Existence and regularity of solutions for an evolution model of perfectly plastic plates

TL;DR

This paper extends the analysis of a dynamic model for perfectly plastic plates by incorporating external forces and investigates the regularity of solutions, showing that stress derivatives are locally square integrable.

Contribution

It introduces external forces into the evolution model and proves regularity results for the stress tensor derivatives.

Findings

Existence of solutions with external forces.

Stress derivatives are locally square integrable.

Enhanced understanding of solution regularity.

Abstract

We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model, and we discuss the regularity of the solutions thus obtained. In particular, we show that the first derivatives with respect to space of the stress tensor are locally square integrable.